Servo system employing switching type feedback

ABSTRACT

The invention provides a servo control system, capable of either a continuous or discontinuous operating mode, which utilizes sign-switched integration circuit to obtain extremely fast response under an unusually wide range of operating conditions. Two internal feedback quantities are employed, one of which comprises the output control signal and the other of which is the output of an integrator whose input is connected to a circuit element which generates a positive or negative value of the first time derivative of the output control signal and whereby the sign of this first time derivative is made dependent upon variables of the system. The application of the invention to a spacecraft navigation system is described.

O United States Patent 1191 n 3,710,086 Lahde et al. 451 Jan. 9, 1973[54] SERVO SYSTEM EMPLOYING OTHER PUBLICATIONS SWITCHING TYPE FEEDBACKHiltz: Adaptive Autopilot from Aerospace Electronics, [75] inventors:Reinhard N. Lnhde, Los Altos; Alex Sept. 1960; Vol. 34, p. 130134.

pll'lclek, Granada Hills. both 0f McLaren: A Gas-Jet Altitude-ControlSystem. Con- C trol, Sept, 1964, Vol. 8, p. 446-450.

[73] Assignee: Lockheed Aircraft Corporation, Los

Angel, Calm Przmary ExammerFehx D. Gruber Attorney-George C. Sullivanand Ralph M. Flygare [22] Flled: Feb. 5, 1970 Appl. No.: 8,934

[57] ABSTRACT The invention provides a servo control system, capable ofeither a continuous or discontinuous operating mode, which utilizessign-switched integration circuit to obtain extremely fast responseunder an unusually wide range of operating conditions. Two internal feedback quantities are employed, one of which comprises the output controlsignal and the other of which is the output of an integrator whose inputis connected to a circuit element which generates a positive or negativevalue of the first time derivative of the output control signal andwhereby the sign of this first time derivative is made dependent uponvariables of the system. The application of the invention to aspacecraft navigation system is described.

10 Claims, 7 Drawing Figures PATENTEUJMI 9mm 3.710.088

sum 1 nr 4 INVENTORS REINHARD N. LAHDE ALEX PAWELEK Agent PATENTEDJM 9I973 SHEET 2 UF 4 mvswroRS REINHARD N. LAHDE ALEX PAWELEK FIG- 3PATENTEU JAN 9 I973 SHEET LL 0F 4 FIG- 6 ITII INVENTORS REINHARD N.LAHDE ALEX PAWELEK Age nt SERVO SYSTEM EMPLOYING SWITCHING TYPE FEEDBACKBACKGROUND OF THE INVENTION Various types of on-off" or switching-typeof servo control systems have been proposed heretofore. Systems of thistype find a unique contemporary application as attitude and maneuveringcontrol systems for missiles and spacecraft, since these vehicles areunusually demanding in terms of economy and performance. These priorsystems, sometimes referred to as bang-bang systems, while superior inmany respects to proportional-type control systems, have suffered from anumber of deficiencies such as undesirable damping, steady-state error,and response time lag. These deficiencies of prior switching-typesystems are overcome by the present invention which employs an auxiliaryfeedback voltage utilizing sign-switched integration. The system of thepresent invention may be broadly classified as a control of the"bang-bang type in which off-on or discrete switching is employed ascompared with continuous proportional control.

In servo control systems, employing feedback, it is customary to usesystem output and/or system error for dynamic stabilization. If thesystem is linear, a first derivative or a combination of first andhigher order derivatives of system output and/or system error is oftenused. The present invention is based upon a concept of time-switchedintegration and is applicable to both linear and certain types ofnon-linear control systems.

SUMMARY OF THE INVENTION Summarizing, the invention comprises a noveland improved servo control utilizing a switching-type feedback methodand sign-switched integration, to obtain extremely fast response, andwhich will operate effectively under an unusually wide range ofconditions.

The switching logic of the invention may be termed conditionalswitching. This technique provides for the generation of an auxiliaryfeedback voltage through integration of the first and/or higherderivatives of the function to be controlled, for example theangularattitude of a spacecraft as may be represented by a DC voltageproportional to said attitude, whereby the sign of the signalrepresenting said function to be integrated is reversed at certain timesdepending on system condition. One basic property of the auxiliaryfeedback voltage is that it becomes zero when a signal proportional tothe rate of the controlled variable is zero. The system of the inventionprovides an increase in the speed of response as compared with priorsystems, and in certain practical constructions the attainable responsetime is very close to the fastest response theoretically possible orachievable within the limitations of available power in the system.

To facilitate teaching the principles of the invention its applicationto a single-degree-of-freedom attitude and maneuvering control system,employing off-on, constant-thrust reaction jets, for a space vehiclewill be described hereinafter.

By comparison with existing methods of discontinuous control, thetime-switched integration system of the present invention providesgreater system simplicity, faster response, and improved economy of theenergy controlled by the system. Further, it is unusually flexible andcan be adapted to a variety of control situations, as will becomeapparent hereinafter. Also, in certain embodiments, using actual sensorinformation, the system is self-adaptive in the sense that feedbackgains are unity and independent of discrete or slow time (as comparedwith one response cycle) changes of control acceleration.

In contrast to proportional systems, switching-type control systemsachieve their accuracy of control by the timing accuracy of theswitching pulses, in addition to the accuracy of the level of constantacceleration applied. Obviously with a given timing error, the totalsystem error will increase with the number of switching operationsoccurring per unit time. Therefore, the frequency of switching should bekept as low as is compatible with other dynamic control requirements.

Of the prior systems mentioned above, pulse modulation is one of theoldest methods of discontinuous control. Pulse modulation systems ofswitching logic may be considered as a linearization of the pulse systemin that a quasi-proportional signal is generated in the circuit by asequence of plus, zero, and minus pulses which are timed such that aneffective average level is produced equivalent to a proportional signal.One important design aspect of such a system is the switching frequency.The lowest frequency permissible is limited by undesirable systemresponse to the cycling. Very often, an undesirably large and randomtime-lag occurs if the cycling does not respond to sudden changes ofinput. For example, if a strong pulse-input arrives at a time when thepulse modulator is in the minus cycle, or off cycle, system response maylag the input signal by a substantial portion of the pulse repetitiontime. To avoid this disadvantage, the switching logic of a system shouldbe such that a signal which exceeds the system deadband penetratesdirectly to the decision element for immediate action. The presentinvention provides a novel method and means for achieving thisobjective. Additional objectives will become apparent hereinafter.

A principal object of the invention is to provide a novel and improvedservo system employing switchingtype feedback.

Another object of the invention is to provide a novel and improved servosystem of the discontinuous control type.

Yet another object of the invention is to provide a novel and improvedservo control system employing feedback which utilizes time-switchedintegration.

It is yet another object of the invention to provide a novel andimproved attitude and maneuvering control system for space vehicles.

Still another object of the invention is to provide novel and improvedmeans for obtaining an auxiliary feedback voltage utilizingsign-switched integration for the purpose of controlling a servo system.

A general object of this invention is to provide a novel and improvedservo control which overcomes disadvantages of previous means andmethods heretofore intended to accomplish generally similar purposes.

Other objects of the invention will in part be obvious, and will in partappear hereinafter.

Many other advantages and features of the present invention will becomemanifest to those versed in the art upon making reference to thedetailed description which follows and the accompanying sheets ofdrawings in which preferred structural embodiments incorporating theprinciples of the present invention are shown by way of illustrativeexample.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a servocontrol system of the type employing time-switched integration;

FIG. 2 illustrates, in diagrammatic form, a simple attitude andmaneuvering control system of a space vehicle;

FIG. 3 is a block diagram of a simplified embodiment of the invention;

FIG. 4 is a simplified block diagram of an embodiment of the inventionfor implementing velocity control;

FIG. 5 is a simplified block diagram of a horizontal distance controlembodiment of the invention;

FIGS. 6 and 7 are block diagrams of simplified control systems accordingto the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS SI-IOWN To facilitate expositionof the invention its application to an attitude control system willfirst be described. In this application the reaction jets are operatedwith constant thrust in an on-off fashion. For the sake of simplicitythe system under consideration has been limited to thesingle-degree-of-freedom case and to vehicles operating outside theatmosphere; i.e., the vehicle controlled has no natural damping and noaerodynamic stability.

Inasmuch as each of the functional units represented by a block in thefigures may be any one of the numerous devices for each respectivefunction well known in the art, it is deemed unnecessary to show circuitdetails.

I-Ieretofore, the implementation of switching-type control systems foruse with reaction motors have employed mechanical components for valvingfuel into the reaction motors. In these prior systems, relays have beenused employing electrical contacts for switching power to solenoidswhich in turn open and close the fuel valves. More recentlyelectro-mechanical relays have been replaced with their solid-stateequivalents. To facilitate exposition of the present invention and tosimplify the switching logic, the discussion which follows employsdiagrams and circuits including numerous relays. It should beunderstood, however, that practical implementation of such switchingsystems, for a spacecraft would in most instances employ solid-stateequivalents of the relays shown. Regarding switching logic design thereare two main considerations: performance and weight economy. It is quiteobvious that in order for a switching-type control system to beeconomical of fuel it must use long off cycles whenever possible, andshould never rapidly switch from plus to minus acceleration. Any systemoptimization involves a tradeoff between economy and performance whichdepends on a number of heterogeneous operational and mission parameters.

The present invention is, in broadest terms, a feedback system. Feedbacksystems of the type to which the present invention belongs may also bereferred to as race-brake systems and such systems may be designed formaximum performance, i.e., fastest response, by taking maximum advantageof the capabilities of a switching-type control regardless of inputlevel. Assuming that the input is a step input, systems of this typewill accelerate towards diminishing error with full acceleration untilarriving at a point where the combination of error remaining and thesystem rate is such so as to require full deceleration in order to cometo a stop at zero error, provided that the input has not changed duringthe braking period. The optimum response of such a system need not berestricted to step inputs. That is, the system also responds in anoptimum way to a ramp input in that regardless of the steepness of theramp input signal, the system output achieves a rate equal to that ofthe ramp in the shortest time compatible with the systems powerlimitation. Prior systems of this general type have a velocity error,however, like other control systems. For example, linear systems havevelocity errors unless error integration is used. Error integration canalso be applied to the race-brake systems as well as to the system ofthe present invention.

The system now to be described may be referred to as a time-switchedintegration system. The system is shown in FIG. 1 and has a decisionamplifier I where the input 6, on line 2 is compared with two feedbackvoltages 6 and 0; on lines 3 and 4, respectively, one being the systemoutput, i.e., 0, the other one here termed auxiliary feedback voltage 0The output of decision or adding amplifier 1 appears on line 5 and issupplied to switching element 6. Switching element 6 has a specifieddeadband and is so constructed that when the input signal amplitudeexceeds the deadband, the output f) on line 7 assumes a value of +1: ora depending on the algebraic sign of the input on line 5. The outputsignal 0 is supplied to both integrator 8 and to polarized relay 9. Theintegrated output from integrator 8 appears on line 11 and is suppliedvia diode 12 to amplifier 13, and via amplifier 14 and diode 15 toamplifier l3. Amplifiers l3 and 14 are inverting unit gain amplifiers.

Integrator 16 is connected to the output of integrator 8 via line 10 andtherefore integrates vehicle rate of produce vehicle attitude 0 on line3. to input to integrator 17 is obtained via relay arm contact 18. Relaycontact 19 is supplied from diodes l2 and 15, and relay contact 21 issupplied from the output of amplifier 13.

System operation is best understood by assuming a step input on line 2.The system performs an acceleration towards decreasing error. Duringthis cycle, the auxiliary voltage Or on line 4 is developed byintegrating attitude rate and, therefore, equals the voltagerepresenting system attitude 8 on line 3. This is because 18 isconnected to contact 19 which carries a voltage equivalent toi 0| andsince 6 is positive, l; l equals 0. The two voltages (on lines 3 and 4)therefore add up at the decision amplifier 1 to produce twice the effecton the output 5. This has the consequence of zeroing the decisionamplifier 1 when the system has travelled an amount equal to one-half ofthe original step error. At this time, the decision amplifier output (5)becomes slightly negative and the braking cycle begins, because relaycoil 9, now obtaining negative voltage, causes arm 18 to travel tocontact 2 l. This switching action reverses the sign of function 0 whichis the input to integrator 17 which generates 6,. This has theconsequence that the sum of the output plus 0 remains constant duringthe braking period by keeping the decision amplifier output slightlynegative and maintaining negative accelerations until system error anderror rate vanish simultaneously.

For a full understanding of the operation of the system it is helpful toalso consider a negative step input on line 2. in this case, thedecision amplifier l and the switching element 6 become negativelybiased and relay coil 9 causes contact 18 to move to contact 21. Becauseof the negative system acceleration, a negative feedback voltagedevelops on line 3. This voltage is fed into the decision amplifier 1with an opposite sign, i.e. it opposes the negative step input voltageon line 2. Simultaneously, a negative auxiliary voltage o is developedon line 4 by integrating a negative value of the absolute attitude rate,because contact 18 is connected to contact 21 which, through the actionof sign reversing, unity gain amplifier 13 carries a negative value ofthe absolute attitude rate developed on line 19. The two voltages online 3 and 4, being both negative, add up at the decision amplifier l toproduce twice the effect on the output 5. This again has the effect ofzeroing the decision amplifier 1 when the system has travelled an amountequal to one-half of the original negative step input. At this time, thecombined action of the two negative feedback voltages which enter thedecision amplifier 1 with an opposite sign, i.e. as positive voltages,become larger than the negative input voltage, which causes the outputof the decision amplitier 1, i.e., line 5, to carry a slightly positivevoltage. At this time, the relay coil 9 causes arm 18 to move to contact19, thereby making the input to integrator 17 positive. At the sametime, the system acceleration, i.e. line 7, has become positiveindicating that the braking cycle has begun. Now, consider that linecarries a voltage of the same magnitude, but of opposite sign, as line22. Both voltages are integrated and combine at the decisionamplifier 1. As a result, the sum of the output 0 plus 0 remainsconstant during the braking period and keeps the output of the decisionamplifier 1 slightly positive, which in turn maintains positive systemacceleration until system error and error rate simultaneously becomezero.

It is, of course, easily possible to introduce a deadband for fuelsaving, as indicated in FIG. 1, but which so far had not been consideredin the explanation of the functioning of the circuit. 1f the deadband isdenoted as t 0,, and the relay 9, 18, 19, 21 is so constructed thatwhenever the absolute value of the output of decision amplifier 1, i.e.the voltage on line 5, is smaller than the deadband voltage, the arm 18will be positioned midway between 19 and 21, i.e., zero voltage will befed into the integrator 17. With these stipulations the control lawsgoverning the operation of this system are as follows:

a =0 if5=0 a is the systems acceleration capability, a constant value.

As can be seen, an advantage of this switching logic is that nomultiplication need be implemented. Also, both feedback signals, 0 and0)? have unity gain; hence optimal system operation is maintained evenin the presence of changes of the system s acceleration capability a, aslong as the change is sufficiently slow such that the accelerationduring the first half of a cycle in response to a step input signal isnot significantly different from the deceleration during the second halfof that cycle.

As noted above, an important feature of this system is that nomultiplication is necessary in the switching logic, thus simplifying thesystem. A more important feature is the fact that the feedback gain doesnot contain a scale factor; therefore, the feedback gain is unity, andthis feature is maintained even in the presence of slow changes of levelof the system acceleration. [t is therefore justified to term the systemadaptive. This feature is of particular importance for spacecraftattitude control systems where the decrease in vehicle mass due to fuelconsumption tends to progressively decrease the moment of inertia andhence increase the angular acceleration capability of the reactioncontrol system used for attitude control.

One of the characteristics of the auxiliary feedback voltage or is thatmathematically it must be zeroed whenever the system output rate iszero. This property holds for all modifications of the system which, aswill be discussed later, may include deadband, proportional off" time,velocity limitation, etc. Obviously, to practically maintain thisfeature would require the integrator which produces O not to have anydrift. A simple zeroing circuit may be employed to zero the output ofthe critical integrator whenever the system rate goes through zero,thereby making the drift requirement for the integrator very moderate.

The time-switched integration system is very flexible in that it can beadapted to many additional operational requirements. A few exemplarymodifications will be discussed hereinafter. The introduction of adeadband is very simple and merely involves a zone of insensitivity inthe main decision amplifier and is done in the same manner as withconventional systems. The only additional feature which must be providedin the circuit whenever "05" times are involved is that the input of theintegrator generating the auxiliary feedback voltage must be zeroed forany period of zero system acceleration.

There is shown in FIG. 2 an attitude and manuevering control system 20for a spacecraft 23 hovering at a given location. The control systememploys reaction jets 24 and 25 which can be controlled only for zero orfull thrust, hence an angular acceleration of the spacecraft 23 can beobtained having only three possible values, zero, plus a, or minus a,where a is the angular acceleration capability of the system, i.e. a TU]. The term I is the moment of inertia of the vehicle about its centerof gravity and the axis of rotation concerned. It is further assumedthat the main thrust, T,,, obtained from jet 26 is controlled tocounteract the weight of the vehicle so as to maintain constantaltitude.

FIG. 3 is a block diagram of the attitude control system 20 forspacecraft 23 which utilizes the feedback method and apparatus of theinvention. In the embodi ment of FIG. 3, the sign of amplifier 27,corresponding to decision amplifier 1 of FIG. 1 determines whether plusor minus acceleration is to be applied. In the interest of simplicity,the deadband" is disregarded, which in practice would be introduced forzero command. Relay 32 and contacts 39, 43 and 44 correspond to theswitching element 6 of FIG. I. A pitch attitude command 0. is applied oninput line 28.

The fastest possible way for the spacecraft 23 to respond to a stepinput command (0,) of attitude would be to apply positive accelerationuntil one-half of the desired attitude change has been achieved, thenswitch to minus acceleration for an equal amount of time and then zerothe system. In order to accomplish this automatically, amplifier 27receives two feedback voltages, termed 0., (on line 29) and O (on line31). The signal 0 is the actual attitude of the vehicle, appearing as avoltage signal; O is the auxiliary feedback voltage in accordance withthe method of the invention. It is obtained by integrating attitude ratebut, switching sign of integration when the system switches the sign ofthe angular acceleration.

The output of decision amplifier 27 is used to energize the polarizedrelay coil 32. Arm contact 33 is actuated by relay coil 32 and serves toswitch a positive voltage, supplied on line 34 from any suitable source,to either contact 35 or 36. When the output of 27 is positive, as shownin FIG. 3, contact 35 is closed and power will be supplied on line 37 toturn on jet 24 of the spacecraft 23 (see FIG. 2). When contact 36 isclosed, power will be applied to line 38 causing jet 25 to be turned on.

Relay coil 32 also operates arm contacts 39 and 41. Arm contact 39 willapply a positive voltage to integrating amplifier 42 when closed tocontact 43, and will supply a negative voltage to amplifier 42 whenclosed to contact 44. The output of integrating amplifier 42 is suppliedon line 45 to the input of integrating amplifier 46 and also to relaycoil 47.

The relay 47 with the contact arms 48, 49 and the contacts 51, 55, 56,57 and the inverting unity gain amplifier 54 constitutes an alternateway of generating the absolute value of 6 on contact 52, and itsnegative value at 58. In FIG. 1, the absolute value of 0, and itsnegative value was generated instead by means of the rectifiers 12 andand the inverting unity gain amplifier 13, whereby the relay switch 18,19, 21 of FIG. 1 corresponds in FIG. 3 to the relay switch 41, 52, and58. Otherwise, the circuit of FIG. 3 and its functioning is the same asthat of FIG. 1.

As can be seen in FIG. 3, three voltages are fed into amplifier 27.During the first half of the cycle, the sum of two feedback voltages, 190,- (appearing on lines 29 and 31 respectively), rises sharply to equalthe input at the proper time for switching. At this time, the output ofamplifier 27 becomes zero (actually slightly negative to get out of thedeadband); during the second half of the cycle, the sum of the twofeedback voltages is a constant value, and therefore minus accelerationis applied during this cycle. At completion of the cycle, the auxiliaryfeedback voltage 0, has decayed to zero, and the position feedbackvoltage 6,, matches the input 0,. The system is now in the same state ofreadiness for another command as it was at the beginning of the stepinput.

The voltage applied to the integrating amplifier 42 via arm 39 contact43 and 44 represents the vehicles angular acceleration. In practicalconstruction this voltage should be made proportional to the actualvehicle acceleration which might be subject to changes, for example dueto the change of the vehicles moment of inertia (fuel consumption,staging), or because of intentional switching of the force level of thevehicle 's attitude control system. For example, the input of theintegrator 42 could be connected to the output of a vehicle mountedangular accelerometer. This would ensure proper functioning of thecircuit even under greatly varying angular acceleration capability ofthe vehicle and thus the system could be termed adaptive.

The feedback method employed in the abovedescribed system may besummarized as follows:

A decision amplifier (27) receives an input command plus two feedbackvoltages, one being the quantity to be controlled, the other, calledauxiliary feedback being obtained by integrating the first derivative ofthe control function but reversing the sign of the integration when theoutput of the decision amplifier changes its sign. This method ofobtaining the auxiliary feedback voltage is referred to as sign-switchedintegration".

The method of the invention may further be illustrated by anotherexample for obtaining velocity over ground control. Referring again toFIG. 2 the objective is now to convey to spacecraft 23 a desiredvelocity over the ground. Since thrust is maintained to keep thealtitude of the spacecraft constant, tilting the spacecraft generates alongitudinal acceleration, 35 which is equal to gravity multiplied bythe tangent of pitch angle or, for small tilt angles simply proportionate to that angle.

FIG. 4 is a block diagram of apparatus for implementing velocity controlin accordance with the invention. The block identified as attitudecontrol 61 corresponds to the control system 20 shown in FIG. 3.Decision amplifiers 62-64 are utilized in the circuit to generate switchpositions T or Z, depending on the signs of their output. Amplifier 63is the main decision element, (corresponding to amplifier 27 in FIG. 3),i.e., it receives the three feedback voltages as explained in theprevious case. In this case, the auxiliary voltage in. is obtained bysign switched" integration of 55 The output of the attitude control 61is supplied to multiplier (potentiometer) which applies a gravity factorto the vehicle attitude control signal 8 on line 59 to give the outputsignal it], on line 70. The signal on line 70 is supplied to integratingamplifier 80 and also to relay contacts 65 and 66. This signal is alsosupplied to sign changing amplifier 67. Additionally, the signal it}, issupplied to integrating amplifier 68 via contact 65, arm contact 69,contact 71, and arm contact 72, when the switch position T exists. Thesign of the signal is reversed via sign changing amplifier 67, andappears at contacts 73 and 74. Alternate logic for the Z switch positionis provided via contact 74, arm contact 75, and contact 76. The feedbackvoltage h from integrating amplifier 68 is supplied to main decisionamplifier 63 on line 77. The output of main decision amplifier 63energizes relay coil 78 via contacts 79 and 81 in the T switch position,and via sign changing amplifier 82 and contact 83 in the Z switchposition. The T or Z switch positions are controlled by relay coil 84which in turn is energized by the output of decision amplifier 64.

Relay coil 78 operates switch contacts 85-88 as well as contacts 71, 72and 76. The velocity command signal on line 92 is sent via contacts 85and 86 to the input of attitude control 61 via limiter 91 where itappears as a voltage representing attitude. An additional feature of theinvention is the ability to limit the maximum tilt angle and thus themaximum acceleration over the ground, i.e., the first derivative of thefunction to be controlled. This circuit (91) automatically limits themaximum tilt angle of the spacecraft to some predetermined value, say40. The feedback signal i is supplied to decision amplifier 62 via unitygain amplifier 93 and contacts 87 and 88. This signal i also appearsacross capacitor 89 which is referenced to ground 90.

The reason why this circuit is slightly more complicated as comparedwith the one in FIG. 3 is that the response characteristic ofquantity-to-be-controlled, as a function of an input into the attitudecontrol 61 is different. The principle of operation of this circuit isas follows: A step input x, from the pilots control stick generates anunbalance in amplifier 63, causing contacts 85 and 86 to close, contacts87 and 88 to open, and 72 to go to T (71). This puts the step inputvoltage at the input of the attitude control 61 where it is translatedinto an attitude command. The spacecraft goes through the cycling of itsreaction control system in accordance with the mechanics of the circuitFIG. 3 and achieves the desired pitch angle precisely at the time, whenone half of the commanded speed over ground is achieved. At this time,in accordance with the feedback principle of the invention, the outputof amplifier 63 changes sign, causing contacts 85-86 to open, contacts87-88 to close, contact 72 to go to Z (76). Now, the attitude control 61sees a zero command and causes the vehicle attitude to return to zero.At the same time, the achieved velocity, i.e., a voltage representingsame, respectively, is applied to amplifier 62 via contacts 87-88. Aftercompletion of the cycle, the spacecraft has achieved the commandedvelocity, i.e., output of amplifier 62 is zero. Output of amplifier 63is likewise zero, since in accordance with the method of feedback of theinvention, i,- has also integrated back to zero. The system is new againin a state of readiness for another command.

As can be seen from the foregoing example, the timeswitched integrationmethod of the invention is not restricted in application tosingle-degree-of-freedom attitude control. The higher order control taskperformed by the apparatus of FIG. 4 permits maneuvering during thehovering period by tilting the spacecraft around one of twoperpendicular horizontal axes, thereby generating sidewise accelerationsequal to gravity acceleration multiplied by the tangent of the tiltangle 9. The apparatus of FIG. 4 comprises only one axis. The inputsignal it, may be derived from a pilots control stick. Upon deflectionof the control stick, the system automatically goes through a series ofacceleration and deceleration maneuvers which establish the commandvelocity over the ground in the shortest possible time compatible withsystem angular acceleration capability and the maximum permitted tiltangle.

In explaining the principle of feedback of the invention, a step inputhas been assumed in both examples, and the cycling of the circuit hasbeen followed until the spacecrafts output matched the input command. Itshould be understood, however, that the system is capable of appropriateoperation for inputs other than step inputs or in case a new step inputis applied to the system on top of the old one, before the system hashad time to complete its cycle in response to the first input. In allcases, the system is capable of generating the fastest vehicle responsecompatible with the basic limitation of the reaction control system.

The method of feedback in accordance with the invention is notrestricted to the two examples of FIGS. 3 and 8. FIG. 5 is anotherembodiment of the invention, using the same principle, for control ofhorizontal distance of a space vehicle. This embodiment also illustratesan additional feature possible with the present invention. If it isdesired to place a limitation on the magnitude of the first derivativeof the quantity to be controlled, then this limitation can be obtainedby the circuit shown in FIG. 5 wherein the quantity to be so limited isvelocity over ground. In this case it is shown to be limited toSOlsecond. This requires the voltage limiting devices (127 and 128)shown in front of function 4), and after (118 and 119) the integrator115, generating x In this case, block corresponds to the velocitycontrol circuit shown in the schematic of FIG. 4.

The remainder of this circuit is substantially the same as the circuitof FIG. 4. However, this circuit does not include the gravity factorelement but is additionally provided with the limiters mentionedhereinabove. The output of velocity control 100 is supplied via line 94to integrating amplifier 95, sign changing amplifier 96, and contacts 97and 98. The input command is supplied on line 99 to decision amplifiers101, 102 and 103. The output of decision amplifier 102 controls relaycoil 104, via contacts 105 and 106 in the T switch position, and viacontacts 106 and 107 in the Z contact position, by way of sign changingamplifier 108. Arm contact 106 is controlled by relay coil 109 which inturn is energized by the output of decision amplifier 103. Relay coil109 also operates contacts 1 l l and 112 which transfer the feedbacksignal to contacts 113 and 114. Integrating amplifier 115 receives itsinput signal via contact 1 16, and its output appearing on line 117 islimited by clamp diodes 118 and 119 which are connected to a suitablereference voltage source (not shown). The output signal on line 117 isthe feedback signal x and in a typical construction may have itsamplitude limited by diodes 1 18 and 1 19 to correspond to a maximum ofi 200', Le, the stopping distance when travelling at a steady state witha maximum velocity of 50'lsecond.

Relay coil 104 operates contacts 116, 121-124. The feedback signal x issupplied via contacts 121 and 122 to unity gain amplifier 125 and tocapacitor 126.

The output signal from amplifier 101 is limited via diodes 127 and 128prior to being fed to velocity control 100. Limiting diodes 127, 128limit the maximum velocity to flOlsecond. The signal on line 129corresponds to i Referring to FIG. 6 there is shown a simplified circuitwhich will also function in accordance with the control laws previouslystated. This circuit is similar to that in FIG. 1 but utilizes only one,instead of two, reversing amplifiers and employs no diodes. Instead, aspecial type of polarized relay is used, one whose polarization isproduced by means of an electromagnet rather than a permanent magnet,and whereby the coil 133 which magnetizes the electromagnet is connectedto the input of the integrator 134 and the coil 140 which magnetizes thearmature is connected to the output of the integrator 134. Operation ofthe circuit of FIG. 6 is very similar to that of FIG. 1. With a positivestep input, the output of the switching element 133 is at first positiveand this results in both the input and the output of the integrator 134to be at first positive. This causes arm 138 to move to contact 137 andboth integrators 146 and 145 develop identical, positive voltages,representing the system output. Therefore, when one-half of thecommanded step input is reached, the output of the adding amplifier 131begins to turn negative which causes the switching element 133 toproduce a negative output, indicating the beginning of the brakingcycle. It also causes arm 138 to move to contact 136 and the integrator145 now integrates the negative system rate, thereby keeping the outputof the summing amplifier 131 slightly negative until system error andsystem rate simultaneously become zero.

With a negative step input the arm 138 also initially moves to contact137. This is because in this case the input as well as the output ofintegrator 134 are both negative. That is to say, in the polarizedrelay, both the polarization and the armature magnetization havereversed their polarity as compared to the case of a positive stepinput. The integrators 146 and 145 again develop identical, but thistime negative voltages, again representing system output and againopposing the now negative input voltage. When one-half of the commandedstep input is reached, the output of switching element 133 changes signfrom negative to positive thereby producing unequal signs of the twovoltages enterin g the polarized relay. Therefore, the arm 138 movesfrom contact 137 to contact 136 at this time, causing the auxiliaryfeedback voltage to decay to zero and the output of the summingamplifier 131 to remain slightly positive until system error and systemrate simultaneously have become zero.

FIG. 7 shows still another embodiment of the attitude control system ofthe type previously shown in FIG. 1. The operation of this circuit, forthe case of a positive step input, should be immediately clear fromcomparison with the circuit of FIG. 1. Since the system, whileresponding to a positive step input, will exhibit a positive angularrate the solenoid operating switch 141 will, during this time, beenergized by a positive voltage which is the output of integrator 134(integrator 8 of FIG. 1). With a negative step input, the differencebetween the two circuits will be readily apparent; whereas in thecircuit of FIG. 1 all sign switching is done ahead of the integratorproducing the auxiliary feedback voltage (integrator 17 of FIG. 1), inthe circuit of FIG. 7, the basic sign switching of the auxiliaryfeedback voltage in response to the sign of the system rate is donedownstream of the integrator which produces the auxiliary feedbackvoltage, 144. Thus, with a negative-step input, the time history of theauxiliary feedback voltage will be the same as for a positive stepinput, only reversed in sign. Note that the switching of contact 141between 142 and 143 occurs only when system rate goes through zero, atwhich time in accordance with the previously set forth control laws(equation 6), the auxiliary feedback voltage is also zero. For thisreason, the auxiliary feedback voltage will never experience adiscontinuity as a consequence of the switching, as might be suspectedon first inspection of the circuit FIG. 7.

As can be seen from the foregoing there has been shown and described anovel servo control system utilizing sign-switched integration. Whilethese systems have been illustrated in embodiments particularly adaptedto the reaction motor control systems of a spacecraft, it will beapparent to those versed in the art that these systems have a much widerrange of applicability. Furthermore, it will be obvious to those versedin the art that certain changes may be made in the method and/or theapparatus of the invention without departing from the scope of theinvention herein involved. Since it is understood that variousomissions, and substitutions, and changes in the form and details of thedevices illustrated, and in their operation, may be made by thoseskilled in the art, without departing from the spirit of the invention,it is intended that the invention be limited only as indicated by thescope of the following claims.

What is claimed is: 1. A closed-loop servo control system comprising:means for receiving a system input signal representing a desired stateof a quantity to be controlled;

means for providing a system output signal representing the actualmeasured state of said quantity to be controlled;

first and second feedback signal circuit means, connected to said systeminput signal receiving means, carrying corresponding first and secondfeedback signals which are subtracted from said system input signal toproduce an error signal, at the output of said system input receivingmeans, representing the difference between said desired state and theactual state of said quantity to be controlled;

means for supplying said system output signal to said first feedbacksignal circuit;

means for generating a signal representing a first time derivative ofsaid quantity to be controlled; means for reversing the sign of saidfirst time derivative signal;

switching means having first and second operating conditions asdetermined by the magnitude and sign of said error signal; and,

integrating means having an input for receiving the signal produced bysaid first time derivative generating means in response to the firstoperating condition of said switching means, for receiving the signalproduced by said sign reversing means in response to the secondoperating condition of said switching means, and having its outputconnected to said second feedback signal circuit whereby said systeminput signal is modulated in a manner as to force said quantity to becontrolled to approach said desired state.

2. A closed-loop servo control system as defined in claim 1 including:

second integrating means connected to the output of said first timederivative signal generating means to provide said first feedbacksignal.

3. A closed-loop servo control system as defined in claim 1 wherein saidfirst and second feedback circuit means includes:

control means interposed between said first time derivative generatingmeans and said first feedback signal circuit means for producingessentially a second time derivative of said quantity to be controlled.

4. A closed-loop servo control system as defined in claim 3 including:

means for changing the sign of the output of said first time derivativesignal generating means to correspond to the sign of the second timederivative of said system output signal.

5. A time-switched integration servo system comprising:

an adder having first, second, and third input terminals and generatinga sum signal at its output terminal;

a source of control voltage connected to said first input terminal forsupplying a position command signal thereto;

switching means connected to said output terminal and responsive theretoto generate a fixed voltage having a sign corresponding to the sign ofthe summed output from said adder;

first integrator means having its input connected to said switchingmeans and its output made to act upon said second input terminal, forintegrating said fixed voltage to provide a velocity feedback voltage tosaid adder; and

second integrator means having its input connected to the output of saidfirst integrator means and its output connected to said third inputterminal, for integrating said velocity feedback voltage to provide anauxiliary feedback voltage to said adder, indicative of position.

6. A time-switched integration servo system as defined in claim 5having:

sign changing means interposed between said first integrator means andsaid second integrator means, and responsive to said switching means tochange the sign of the derivative of the position feedback voltagewhenever the sum of said position feedback voltage and said auxiliaryfeedback voltage equals said command signal.

7. A time-switched integration servo system compris ing:

an adding amplifier adapted to receive a command input and two feedbackinputs, and to provide a summed output;

switching means responsive to said summed output for providing a fixedamplitude signal, the sign of which corresponds to the sign of saidsummed output, whenever the sum of said inputs exceeds a predeterminedsignal level above a deadband zone;

a first integrator connected to the output of said switching means forproviding a time integral of said fixed amplitude signal;

a second integrator connected to the output of said first integrator forproviding a signal to one of said feedback inputs;

first sign changing means for obtaining a signal from said firstintegrator which is of opposite sign;

a third integrator having its input controlled by said switching meansfor integrating the output of said first integrating means whenever saidswitching means is providing a positive amplitude signal and forintegrating the output from said first sign changing means whenever saidswitching means is providing a negative amplitude signal; and

means connecting the output of said third integrator to said otherfeedback input.

8. A time-switched integration servo system as defined in claim 7including:

first and second diodes, the anode of said first diode being connectedto the output of said first integrator and the anode of said seconddiode being connected to the output of said first sign changing means,and the cathodes of both of said diodes being connected in common toproduce a positive voltage equal in magnitude to the output of saidswitching means, regardless of the sign of the output of said switchingmeans;

second sign changing means connected to said common cathodes of saiddiodes; and

control means for connecting the input of said third integrator to saidcommon cathodes whenever the sign of said summed output is positive, andfor transferring the input of said third integrator to the output ofsaid second sign changing means whenever the sign of said summed outputis negative.

9. A time-switched integration servo system comprising:

an adder having first, second and third input terminals and generating asum signal at its output terminal;

a source of control voltage connected to said first input terminal forsupplying a position command signal thereto;

first switching means connected to said summed output and responsivethereto to generate a signal voltage having a sign corresponding to thesign of the summed output from said adder;

first integrator means having its input connected to said firstswitching means for integrating said signal voltage;

second integrator means having its input connected to the output of saidfirst integrator means and its output connected to said second inputterminal to provide a feedback voltage to said adder;

third integrator means having its output connected to said third inputterminal for supplying an auxiliary feedback voltage to said adder;

sign changing means having its input connected to the output of saidfirst integrator means; and

second switching means for connecting the input of said third integratormeans to the output of said first integrating means whenever the sign ofthe output of said first integrating means equals the sign of the inputof said first integrating means, and for connecting the input of saidthird integrator means to the output of said sign changing meanswhenever the sign of the output of said first integrating means isopposite to that of the input of said first integrating means.

10. A servo system comprising:

an adding amplifier having a command input, a feedback input, anauxiliary feedback input, and an output generating a sum signal;

switching means responsive to the sum signal of said adding amplifierand having two stable states dependent upon the sign of said sum signaland generating an output of predetermined magnitude;

a first integrating amplifier for integrating the summed output fromsaid switching means;

a second integrating amplifier connected to the output of said firstintegrating amplifier for providing a feedback signal to said feedbackinput;

sign changing amplifier means connected to the output of said firstintegrating amplifier for providing a time integral signal of negativepolarity;

a third integrating amplifier having its output connected to saidauxiliary feedback input; and,

control means responsive to said switching means for connecting theoutput of said first integrating amplifier to the input of said secondintegrating amplifier whenever the sign of said summed output ispositive and for connecting the output of said sign changing amplifierto the input of said third integrating amplifier whenever the sign ofsaid summed output is negative.

i I t l

1. A closed-loop servo control system comprising: means for receiving asystem input signal representing a desired state of a quantity to becontrolled; means for providing a system output signal representing theactual measured state of said quantity to be controlled; first andsecond feedback signal circuit means, connected to said system inputsignal receiving means, carrying corresponding first and second feedbacksignals which are subtracted from said system input signal to produce anerror signal, at the output of said system input receiving means,representing the difference between said desired state and the actualstate of said quantity to be controlled; means for supplying said systemoutput signal to said first feedback signal circuit; means forgenerating a signal representing a first time derivative of saidquantity to be controlled; means for reversing the sign of said firsttime derivative signal; switching means having first and secondoperating conditions as determined by the magnitude and sign of saiderror signal; and, integrating means having an input for receiving thesignal produced by said first time derivative generating means inresponse to the first operating condition of said switching means, forreceiving the signal produced by said sign reversing means in responseto the second operating condition of said switching means, and havingits output connected to said second feedback signal circuit whereby saidsystem input signal is modulated in a manner as to force said quantityto be controlled to approach said desired state.
 2. A closed-loop servocontrol system as defined in claim 1 including: second integrating meansconnected to the output of said first time derivative signal generatingmeans to provide said first feedback signal.
 3. A closed-loop servocontrol system as defined in claim 1 wherein said first and secondfeedback circuit means includes: control means interposed between saidfirst time derivative generating means and said first feedback signalcircuit means for producing essentially a second time derivative of saidquantity to be controlled.
 4. A closed-loop servo control system asdefined in claim 3 including: means for changing the sign of the outputof said first time derivative signal generating means to correspond tothe sign of the second time derivative of said system output signal. 5.A time-switched integration servo system comprising: an adder havingfirst, second, and third input terminals and generating a sum signal atits output terminal; a source of control voltage connected to said firstinput terminal for supplying a position command signal thereto;switching means connected to said output terminal and responsive theretoto generate a fixed voltage having a sign corresponding to the sign ofthe summed output from said adder; first integrator means having itSinput connected to said switching means and its output made to act uponsaid second input terminal, for integrating said fixed voltage toprovide a velocity feedback voltage to said adder; and second integratormeans having its input connected to the output of said first integratormeans and its output connected to said third input terminal, forintegrating said velocity feedback voltage to provide an auxiliaryfeedback voltage to said adder, indicative of position.
 6. Atime-switched integration servo system as defined in claim 5 having:sign changing means interposed between said first integrator means andsaid second integrator means, and responsive to said switching means tochange the sign of the derivative of the position feedback voltagewhenever the sum of said position feedback voltage and said auxiliaryfeedback voltage equals said command signal.
 7. A time-switchedintegration servo system comprising: an adding amplifier adapted toreceive a command input and two feedback inputs, and to provide a summedoutput; switching means responsive to said summed output for providing afixed amplitude signal, the sign of which corresponds to the sign ofsaid summed output, whenever the sum of said inputs exceeds apredetermined signal level above a deadband zone; a first integratorconnected to the output of said switching means for providing a timeintegral of said fixed amplitude signal; a second integrator connectedto the output of said first integrator for providing a signal to one ofsaid feedback inputs; first sign changing means for obtaining a signalfrom said first integrator which is of opposite sign; a third integratorhaving its input controlled by said switching means for integrating theoutput of said first integrating means whenever said switching means isproviding a positive amplitude signal and for integrating the outputfrom said first sign changing means whenever said switching means isproviding a negative amplitude signal; and means connecting the outputof said third integrator to said other feedback input.
 8. Atime-switched integration servo system as defined in claim 7 including:first and second diodes, the anode of said first diode being connectedto the output of said first integrator and the anode of said seconddiode being connected to the output of said first sign changing means,and the cathodes of both of said diodes being connected in common toproduce a positive voltage equal in magnitude to the output of saidswitching means, regardless of the sign of the output of said switchingmeans; second sign changing means connected to said common cathodes ofsaid diodes; and control means for connecting the input of said thirdintegrator to said common cathodes whenever the sign of said summedoutput is positive, and for transferring the input of said thirdintegrator to the output of said second sign changing means whenever thesign of said summed output is negative.
 9. A time-switched integrationservo system comprising: an adder having first, second and third inputterminals and generating a sum signal at its output terminal; a sourceof control voltage connected to said first input terminal for supplyinga position command signal thereto; first switching means connected tosaid summed output and responsive thereto to generate a signal voltagehaving a sign corresponding to the sign of the summed output from saidadder; first integrator means having its input connected to said firstswitching means for integrating said signal voltage; second integratormeans having its input connected to the output of said first integratormeans and its output connected to said second input terminal to providea feedback voltage to said adder; third integrator means having itsoutput connected to said third input terminal for supplying an auxiliaryfeedback voltage to said adder; sign changing means having its inputconnected to the output of saiD first integrator means; and secondswitching means for connecting the input of said third integrator meansto the output of said first integrating means whenever the sign of theoutput of said first integrating means equals the sign of the input ofsaid first integrating means, and for connecting the input of said thirdintegrator means to the output of said sign changing means whenever thesign of the output of said first integrating means is opposite to thatof the input of said first integrating means.
 10. A servo systemcomprising: an adding amplifier having a command input, a feedbackinput, an auxiliary feedback input, and an output generating a sumsignal; switching means responsive to the sum signal of said addingamplifier and having two stable states dependent upon the sign of saidsum signal and generating an output of predetermined magnitude; a firstintegrating amplifier for integrating the summed output from saidswitching means; a second integrating amplifier connected to the outputof said first integrating amplifier for providing a feedback signal tosaid feedback input; sign changing amplifier means connected to theoutput of said first integrating amplifier for providing a time integralsignal of negative polarity; a third integrating amplifier having itsoutput connected to said auxiliary feedback input; and, control meansresponsive to said switching means for connecting the output of saidfirst integrating amplifier to the input of said second integratingamplifier whenever the sign of said summed output is positive and forconnecting the output of said sign changing amplifier to the input ofsaid third integrating amplifier whenever the sign of said summed outputis negative.